5 4- 3 2- 1 2 3 4 5 6

Q: Evaluate the limits as a goes to infinity. (a) lim 5+6+7z² 2+4x²+8x³ 818

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Q: Q3. Prove that V(fg) = gVf + fVg where f and g are functions of x, y. [Make sure you know which…

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Q: Q20 Q21 (15) convergent to Use Macturin series for cos x to find the value of E-1) (A) 1 (B) 0 (C) a…

A: Maclaurin series for f(x) centered at x=0 :         f(x) ≈f(0)+xf'(0) +f''(0)x22!+f'''(0)x33!+...

Q: 23. fsin(Inx) dx = x A) cos(In x) + c. B)-cos(In x) + c. C) sin(lnx) + c. D) -sin(In x) + c. E) -cos…

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Q: Solve the homogeneous equation (x^2+y^2)dx+2xydy=0

A: see below the answer and explanation

Q: Suppose y = sinh Then 1 sinhz z = sin(y) Oaresinh(y) Using implicit differentiation, dy dz (Enter…

A: NOTE: Refresh your page if you can't see any equations. . the given function is here we can write

Q: Q8 09 A)Converge Absolutly 3 B) Diverge Conserge D) Conditionally Converge AWE A) Diverge B)…

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Q: оо 77 -2 2 O 0 sin x dx

A: To evaluate the integral.

Q: 7-10 Sketch the graph of a function f that is defined on R and continuous except for the stated…

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Q: Find the exact value of the distance between the lines 4: x=3+2t, y=−1+4t, z = −6t ₂: x=-1+3s,…

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Q: Find the difference quotient of f(x)=3x^2+5x-2

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Q: 01 The trigonometric A)x-4 zin substitation to evaluate the integral f√16- x³dx in B)x= 16 sind…

A: Given, ∫16-x2dx

Q: -3- q Find the average rate of change of f from x = -1 to x = 2 Give your answer as an integer or…

A: NOTE: Refresh your page if you can't see any equations. . as we can see, the point (-1,0) and (2,-2)…

Q: For the function f(x) = 5x² + 4x, evaluate and simplify the difference quotient. f(x+h)-f(x) h 11

A: NOTE: Refresh your page if you can't see any equations. . substitute x+h for x

Q: a) Find the Laplace Transforms of i. t²u(t-1) te-3tu(t) cos² (wt)u(t). ii. iii.

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Q: Find a formula for the general term an of th assuming the pattern of the first few terms {0, – 5, —…

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Q: e√x, at x = e 9. y = e√x,

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: 9) g(x)=-x³-3x²; Find g(-1) 11) h(n) = 2n - 2; Find h(−3n) in) = -2n² +4+2n; Find g(y - 1)

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Q: Real limits are important whenever you are measuring a(n) O independent O dependent Odiscrete O…

A: Solution: this is one liner answer Ans continuous

Q: Find a linear second-order differential equation F(x, y, y', y") = 0 for which y = c₁x + c₂x² is a…

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Q: Find the following matrix product, if it exists. 368 1 - 4 01 6 7

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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Q: Evaluate the integral.       9x3 1 + x2 dx   PLEASE SHOW STEP BY STEP

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Q: x²y=1+x is a solution to (x²y+k) dx + x³dy=0

A: Topic:- application of derivatives

Q: The curve y2 - x5= -5x is a solution to the differential equation y' = (2x-5)/2y

A: Integrate by seperation of Variables

Q: [x² x cos xdx

A: Integrate: ∫ x2cosxdx

Q: Let f be the function given by f(x) = e + cos x - 1. What is the value of f' (2) ? A (B -1.281…

A: We need to find out the value of f'(2)

Q: dx csc 2xcot 2x S;

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Q: Consider the vector field: V(x,y,z) = (10xy+3, f(x)-7, 0), where f(x) is some function. a) Find…

A: Please see the below pictures for detailed solution.

Q: Solve the following differential equations. Show your complete and detailed solutions. dy xy-y+2x-2…

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Q: The concentration C (in percent) of a drug in a patient's bloodstream. (t) hours after injection is…

A: We can find the answer in the below steps.

Q: a) Calculate the derivative of: f(x) = 2³.cos(3x²) - sinh(3x + √x) b) Give the tangent in the point…

A: solution is given below...

Q: A utility company burns coal to generate electricity. The cost, C(p)C(p)  (in dollars), of removing…

A: NOTE: Refresh your page if you can't see any equations. . the cost function is

Q: (D³5D² + 17D-13)y=0; y(0) = -1, y'(0) = -4;y" (0) = 17 ubstitution and Elimination in Finding the…

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Q: (c) lim 818 75-8 2x³ +3

A: Topic = Limits

Q: In a binomial situation, q = 1 - p. O True O False

A: Solution ) in the binomial situation there are two possible events  p = probability of each success…

Q: Suppose that the function g is defined, for all real numbers, as follows. g(x) = -(x + 1)²+1 if-2…

A: find the function g(x) value at indicated x value.

Q: 90t ²+3 An epidemic is growing in a region according to the rate N' (t) = a. Find a formula for the…

A: Use the integration for finding the N(t) and N(25).

Q: Find the information for the function, f, graphed below. State your answers using interval notation.…

A: NOTE: Refresh your page if you can't see any equations. . as we can see the function is increasing…

Q: 10. 2 S² (y - 1X(2y + 1) dy

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Q: 3. If f(x)=x²+ 10 sin x, show that there is a number e such that f(c)- 1000.

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Q: 2. 2x²y+3ycosx-2c = 0 3. 5y2 + x³y = cx

A: In each of the following, to eliminate the arbitrary constants. 2 2x2y+3y cos x-2c=03 5y2+x3y=cx

Q: ytanx = y'ex

A: Given differntial equation y tanx =y"ex

Q: y" +9y2 cos 3x + 3 sin 3x

A: Please see the below picture for detailed solution.

Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: Slope of a curve y=f(x) at the point (a,b) is given by dydxx=a.

Q: eliminating arbitrary constant y= C1 cos 2x + C2 sin 2x

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Q: y=2x+ce; y'-y = 2(1-x)

A: As we know that; The Sum/Difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 And the common…

Q: In Problems 1 and 2, y = 1/(1+cie) is a one-parameter family of solutions of the first-order DE y'=…

A: Given y'=y-y2 y0=-13

Q: Make a table of values for the equation. y = 1 + √x X 0 1 2 4 9 16 y Sketch a graph of the equation.

A: Consider the equation  y=1+x

Q: Solve for Auxiliary Equation

A: